On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irrevesibility
On the non-linear energy transfer in a gravity wave spectrum Part 2. Conservation theorems; wave-particle analogy; irrevesibility
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DOI：
10.1017/s0022112063000239
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发表时间：
1963-02
影响因子：
3.7
通讯作者：
K. Hasselmann
中科院分区：
文献类型：
--
作者：
K. Hasselmann
从能量和动量守恒的条件出发，证明了本文第一部分讨论的基本四重相互作用的四个相互作用系数都是相等的。然后发现一个进一步的保守量，它可以解释为代表随机海面的重力波集合的数密度。在随机线性波场和质量粒子系综之间的众所周知的类比也被发现在波场中的弱非线性相互作用的情况下成立。波之间能量传递的相互作用条件对应于粒子碰撞的能量和动量守恒方程，波谱变化率的最终方程对应于玻耳兹曼关于碰撞质量粒子系综的数密度变化率的方程。发现与质量粒子系综麦克斯韦分布相对应的驻波谱是简并的。讨论了重力波传递过程的不可逆性问题，但没有完全解决。
From the conditions of energy and momentum conservation it is shown that all four interaction coefficients of the elementary quadruple interactions discussed in Part I of this paper are equal. A further conservative quantity is then found which can be interpreted as the number density of the gravity-wave ensemble representing the random sea surface. The well-known analogy between a random linear wave field and a mass particle ensemble is found to hold also in the case of weak non-linear interactions in the wave field. The interaction conditions for energy transfer between waves to correspond to the equations of energy and momentum conservation for a particle collision, the final equation for the rate of change of the wave spectrum corresponding to Boltzmann's equation for the rate of change of the number density of an ensemble of colliding mass particles. The stationary wave spectrum corresponding to the Maxwell distribution for a mass particle ensemble is found to be degenerate. The question of the irreversibility of the transfer process for gravity waves is discussed but not completely resolved.